The long-term goal is the elucidation of the atomic-level phenomena and mechanisms important to the understanding and ultimate modification of the biological occurrence, function and dysfunction of the apatitie portion of dental hard tissue in vitro and in vivo. The principal emphasis in the current work is on: (1) defects, vacancies, disorder and atomic substitutions in apatites and human tooth enamel, TE, (2) calcium and hydroxyl ion deficiencies, (3) the structural locations, roles and interactions of chlorine, of carbonate, of acid phosphate, and of non-phosphate oxygen, and (4) the atomitic mechanism of the diffusion process in apatite and TE, especially OH diffusion involved in acid dissolution, all in human tooth enamel. In part (1), Zr and one or more of the elements Pb, Na, Mg, K, Zn, and Mn will be studied. The approach in the first three parts involves: (1) the determination of some substitution-interaction features in analog systems with fewer parameters, (2) the deduction of plausible models for the structural locations and roles of the ions and vacancies producing the differences from pure hydroxyapatite, and (3) the selection of the most probable models on the basis of the stringent requirement that they simulataneously account for all known physical and chemical characteristics of the natural material, tooth enamel. Principal tools are X-ray and neutron diffraction, infrared and laser-Raman spectroscopy, deuterizability, and various chemical analysis methods. Particular strength is given to the model assessment and iterative improvement by the use of the poweful new Rietveld whole-pattern-fitting methods of crystal structure refinement method applied with X-ray and neutron powder diffraction data on, here, tooth enamel and synthetic apatites.